cs.CLFeb 26, 2026
SaveHumans and LLMs Diverge on Probabilistic Inferences
Organizations: McGill University · Mila – Quebec AI Institute · University of Vienna · FNRS – UCLouvain ·
Abstract
Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the premise. While reasoning LLMs have demonstrated strong performance on logical and mathematical tasks, their behavior on such open-ended, non-deterministic inferences remains largely unexplored. We introduce ProbCOPA, a dataset of 210 handcrafted probabilistic inferences in English, each annotated for inference likelihood by 25--30 human participants. We find that human responses are graded and varied, revealing probabilistic judgments of the inferences in our dataset. Comparing these judgments with responses from eight state-of-the-art reasoning LLMs, we show that models consistently fail to produce human-like distributions. Finally, analyzing LLM reasoning chains, we find evidence of a common reasoning pattern used to evaluate such inferences. Our findings reveal persistent differences between humans and LLMs, and underscore the need to evaluate reasoning beyond deterministic settings.
Figures & tables
Figure 1: High-level overview of our paper. We use ProbCOPA , a novel dataset of probabilistic inferences, to collect judgments of inference likelihood from humans and models, and study how well their respective judgment distributions align with one another.
Figure 2: Distribution of human responses to ProbCOPA . Top-right: Likelihood scores across the entire dataset are tri-modal, with a significant proportion of responses between these modes; Top-right: likelihood scores for individual items typically follow a truncated normal distribution; Bottom-left: items with median responses towards extreme ends of the scale are subject to lower inter-annotator disagreement than for those in the middle ranges; Bottom-right: items with higher inter-annotator disagreement are (weakly) correlated with loinger response times from participants.
Figure 3: Distribution of likelihood scores across all ProbCOPA items, from three models. In contrast to humans (see Figure 2 ), models rarely return responses indicating medium likelihood, though this tendency is less extreme with GPT-5. See Figure 7 for the full set of distributions by model.
Figure 4: Item-wise comparisons between Gemini-3 and humans. Top-left: median likelihood scores from Gemini-3 align with those from humans at extreme ends of the scale, but not in the middle ranges; Bottom-left: likelihood score distributions from Gemini-3 and humans reflect the same pattern, with highest divergences for middle-range items (which also saw less inter-annotator agreement); Top-right: Gemini-3 shows less response diversity that humans for all items; Bottom-right: Gemini-3 on average reasons longer for items that humans disagree more on.
Figure 5: Distribution of item-wise Wasserstein distances between human and model likelihood score distributions. Ensembling the outputs of all models yields better distributional alignment with human judgments, but still falls short of the human-human baseline.
| Model | Premise | Hypothesis | Reasoning Chain Extract |
|---|---|---|---|
| Kimi-K2-Thinking | The tire on my bike was flat. | I pumped air into the tire. | …When a bike tire is flat, the most common and logical action is to pump air into it… However, there are other possibilities : … They might not fix it at all … They might replace the tube/tire entirely … they might take it to a shop … |
| DeepSeek-R1 | The girl looked pale. | Her father read her a story. | …This is an action a parent might take to comfort a child… However, it’s not the only response. The father might giver her medicine, ask what’s wrong, take her to a doctor, or just let her rest … |
| GLM-4.6 | The man anticipated the team’s victory. | He made a bet with his friends. | …when people anticipate a victory for a team they support, they might be more inclined to bet on that outcome… However … They might not be gamblers … They might not have money to bet … They might be satisfied with just watching the game … |
Table 1: Sample excerpts of reasoning chains from different models, demonstrating the explicit considerations of alternative outcomes of the premise (highlighted in yellow ).
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
| Model Name | Exact Model Version |
|---|---|
| Gemini-3 | gemini-3-pro-preview |
| GPT-5 | gpt-5-2025-08-07 |
| Claude Sonnet-4.5 | claude-sonnet-4-5-20250929 |
| Qwen3 | Qwen3-235B-A22B-Thinking-2507 |
| Kimi-K2 | Kimi-K2-Thinking |
| GLM-4.6 | GLM-4.6 |
Table 2: Exact model versions used in this study.
| Reasoning Effort | Proportion of non-Empty Reasoning Summaries | Range of Total Count of Output Tokens | Mean Differential Entropy of Responses | Median Number of Unique Responses |
| low | 0.000 | 10–10 | -0.486 | 1.0 |
| medium | 0.000 | 10–10 | -0.667 | 1.0 |
| high | 0.198 | 10–250 | -0.296 | 1.0 |
Table 3: Preliminary results from Claude Opus-4.6. Under ‘low’ and ‘medium’ reasoning effort settings, the model always returns empty reasoning chain summaries, with the total number of output tokens being always exactly 10. Under the ‘high’ reasoning effort setting, we see a small proportion of responses include non-empty reasoning chain summaries, and a wider range of output token counts across all model responses. However, we still see almost zero variability in sampled model responses, with the mean differential entropy of item-wise responses being negative (a mathematical quirk of differential entropy on distributions with near-zero variance). Similarly, on average, only one unique likelihood score is provided across the 30 sampled responses for a given ProbCOPA item.
| Persona Type | Persona Prompt Examples |
|---|---|
| Demographic | You are a 23-year-old female barista in Ottawa, who is saving up to backpack across Europe. Your first language is English. |
| You are a 58-year-old male factory worker in Detroit, who is nearing retirement after three decades in the auto industry. Your first language is English. | |
| You are a 36-year-old male taxi driver in Birmingham, who works night shifts to have more time with his young children during the day. Your first language is English. | |
| Psychological | You balance curiosity with pragmatism, comfortable with both the familiar and the new. You are dependable and organized, often making plans to reach your goals. You feel comfortable in both quiet and social settings, adapting as needed. You are caring and cooperative, often attuned to the feelings of those around you. You experience typical ups and downs but manage emotions with balance. |
| You are imaginative and drawn to creativity, often seeking new ways to challenge your thinking. You manage responsibilities reasonably well without being overly rigid. You feel comfortable in both quiet and social settings, adapting as needed. You balance kindness with self-interest, showing empathy without overextending yourself. You sometimes feel self-doubt and worry, but this also makes you sensitive to others’ struggles. |
Table 4: Examples of persona descriptions used in our persona prompting experiments. Demographic persona prompts attempted to simulate some of the demographic variability in our human annotator pool (see Section 2.2 ). Psychological descriptions, on the other hand, attempted to simulate variation in personality. Neither type of persona prompting yielded human-level variation or human-like response distributions (see Figure 15 ).
Figure 6: Overall human likelihood score distribution across (i) five major NLI datasets, collected by Pavlick and Kwiatkowski (2019) , and (ii) ProbCOPA (ours). Likelihood scores collected by Pavlick and Kwiatkowski (2019) for the five major NLI datasets lie on a scale from (hypothesis definitely false given premise) to (hypothesis definitely true given premise). All datasets are subject to tri-modal distributions; but ProbCOPA items receive far more annotations that lie in between these three modes, indicating more graded, probabilistic judgments than for other NLI datasets.
Figure 7: Distribution of likelihood scores across all ProbCOPA items, from all models tested, contrasted against the same distribution from humans. While humans yield an overall likelihood score distribution that is tri-modal, with a large number of responses towards the middle range of the scale, models yield an overall distribution that is bi-modal, with few likelihood scores in the middle range of the scale.
| Reasoning chain length (tokens) Differential entropy of human likelihood scores | Reasoning chain length (tokens) Human response time (log-transformed and -scored) | |||
| Model | Spearman’s | -value | Spearman’s | -value |
| GPT-5 | 0.30 | 7.06e-06 | 0.17 | 1.19e-02 |
| Claude Sonnet-4.5 | 0.18 | 9.61e-03 | 0.12 | 8.74e-02 |
| DeepSeek-R1 | 0.36 | 6.54e-08 | 0.18 | 9.85e-03 |
| Gemini-3 | 0.50 | 2.10e-14 | 0.18 | 9.86e-03 |
| Kimi-K2 | 0.33 | 1.05e-06 | 0.24 | 4.44e-04 |
Table 5: Spearman correlations between reasoning chain lengths and (i) the differential entropy of human likelihood scores, and (ii) human response time, log-transformed and by-participant -scored. While correlations between reasoning chain lengths and human likelihood score entropy suggest a relationship between the two for most models, correlations with human response time are consistently lower. *Grok-4.1 Fast does not return reasoning chain information, and is therefore excluded from this analysis; for Claude Sonnet-4.5, we use the number of output tokens as a proxy for the reasoning chain length, since the latter is not directly provided by the API, and the model’s final output is only a single token in <answer> tags.
Figure 8: Full set of item-wise comparisons of reasoning chain length and differential entropy of human likelihood scores (correlations shown in Table 5 ). Correlations for most models are at least modest ( ), with the highest for Gemini-3. *Grok-4.1 Fast does not return reasoning chain information, and is therefore excluded from this analysis; for Claude Sonnet-4.5, we use the number of output tokens as a proxy for the reasoning chain length, since the latter is not directly provided by the API, and the model’s final output is only a single token in <answer> tags.
Figure 9: Full set of item-wise comparisons of reasoning chain length and human response time, log-transformed and by-participant -scored (correlations shown in Table 5 ). Correlations are consistently lower than when comparing reasoning chain length against human differential entropy. *Grok-4.1 Fast does not return reasoning chain information, and is therefore excluded from this analysis; for Claude Sonnet-4.5, we use the number of output tokens as a proxy for the reasoning chain length, since the latter is not directly provided by the API, and the model’s final output is only a single token in <answer> tags.
Figure 10: Item-wise Wasserstein distances between likelihood score distributions from original human annotators and each model tested, with the same comparison against human baseline annotations. Wasserstein distances between model and human likelihood scores are highest for items with middle-range median scores from humans (which also have the highest differential entropy of human responses). But no such trade-off exists for human-to-human baseline comparisons, which show consistently higher distributional similarity (shown in lower Wasserstein distances) for almost all items.
Figure 11: Item-wise median likelihood scores from original annotations and each of the models tested, along with the same comparison against human baseline annotations. While median likelihood scores from humans and models show some similarity at the two extreme ends of the likelihood scale, this relationship breaks down towards the middle—unlike median scores from our human baseline, which correlate closely with original annotations throughout.
Figure 12: Item-wise differential entropy of likelihood scores from original ProbCOPA annotations and each model tested, along with the same comparison against human baseline annotations. While differential entropy from our human baseline is roughly similar to those from the original annotations, item-level differential entropy of likelihood scores is almost always higher for humans than models.
Figure 13: Results from prompting each of the models tested with different temperature settings. Top row: Distributions of the differential entropy of likelihood scores generated by models for each item. Middle row: Distributions of item-level Wasserstein distances between model and human likelihood score distributions. Bottom row: Proportion of responses with a final likelihood score returned within the maximum token limit (4224). Increasing temperature does lead to more diverse responses from models (top row), and for some models, closer alignment with human response distributions (middle row). But this comes at the cost of far fewer responses containing usable responses (bottom row; many responses at higher temperature values devolve into endless sequences of random tokens).
Figure 14: Results from prompting each of the models tested with different reasoning effort / ‘thinking budget’ settings. Top row: Distributions of the differential entropy of likelihood scores generated by models for each item. Middle row: Distributions of item-level Wasserstein distances between model and human likelihood score distributions. Bottom row: Proportion of responses with a final likelihood score returned within the maximum token limit (4224). Increasing reasoning effort does not appear to lead to any meaningful differences in model likelihood score distributions, as confirmed in Section 4.2 .
Figure 15: Results from prompting each of the models tested, using a different persona each time a response is sampled for a given ProbCOPA item. Top row: Distributions of the differential entropy of likelihood scores generated by models for each item. Middle row: Distributions of item-level Wasserstein distances between model and human likelihood score distributions. Bottom row: Proportion of responses with a final likelihood score returned within the maximum token limit (2048). Having models adopt different personas—whether these personas are based on demographic or psychological profiles (see Appendix D )—does sometimes lead to slightly more response variation, but fails to simulate human-level response variation (top row), nor human-like response distributions (middle row).
Figure 16: Screenshot of the first instructional example presented to participants in our crowdsourced experiment. Participants were shown the general task format, and asked to present a response using the slider. The guide presented beneath the example was intended to align participants on how to use the scale. In this instructional stage, participants were given automatic feedback based on their responses.
Figure 17: Screenshot showing the automatic feedback participants would receive if they provided a likelihood score outside of the ‘likely’ to ‘almost certain’ range for the first instructional example (see Figure 16 ). In this stage, we aimed to use simple examples for which most people would agree on broad likelihood ranges.
Figure 18: Screenshot of the annotation UI for the main phase of the crowdsourced experiment. The UI and task format follow from what participants were shown in the instructional phase. But at this stage, participants have been informed that unlike in the previous phase, there are no ‘right’ or ‘wrong’ answers.
Figure 19: Screenshot of the annotation UI for our validation experiment, in which we slightly vary the prompt wording to closer align with the wording models are presented with (see Section 2.3 ). Note that this variation does not produce different response distributions from our original annotations.
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